Trend-oriented time series modeling with practical application

Abstract

This research compares two types of linear and nonlinear models with a Gaussian error limit. Where these models were used for analysis and forecasting future values of a specific type of time series that represents trending time series. The concept of directional time series has been clarified, and how we can distinguish them from regular series through the skewness test has been explained. We explained that nonlinear models with what is known as the threshold parameter are the best for representing this type of series with prediction. The parameters of the linear and nonlinear models were estimated using the maximum likelihood method. We also conducted several simulation experiments to compare the performance of the models used. To test the best model, statistical criteria were used: the Mean Squared Error (MSE) and the Akaike Information Criterion (AIC) to determine the best model.